For $G$ a simple, connected graph, vertex labeling $f:V(G)\to \Z_+$ is called \emph{radio of $G$} if it satisfies $|f(u)-f(v)|\geq\diam(G)+1-d(u,v)$ for all distinct vertices $u,v\in V(G)$. The number the minimal span over radio labelings $G$. If bijective onto $\{1,2,\dots,|V(G)|\}$ exists, graceful} graph. We determine diameter 3 Hamming graphs and show that an infinite subset them graceful.

Programming languages are enormously diverse, both in their essential concepts and in their accidental aspects. This creates a problem when teaching programming. To let students experience the diversity of essential concepts, the students must also be exposed to an overwhelming variety of accidental and irrelevant detail: the accidental differences between the languages are likely to obscure th...

In this paper, we prove that the square graph of bistar Bn,n, the splitting graph of Bn,n and the splitting graph of star K1,n are graceful graphs. We also prove that the splitting graph and the shadow graph of bistar Bn,n admit odd graceful labeling.

A total labelling of a graph with v vertices and e edges is a one-to-one map taking the vertices and edges onto the set {1, 2, 3, . . . , v + e}. A labelling can be used to define a weight for each vertex and edge. For a vertex the weight is the sum of the label of the vertex and the labels of the incident edges. For an edge {x, y} the weight is the sum of the label of the edge and the labels o...

An $L(h_1, h_2, \ldots, h_l)$-labelling of a graph $G$ is mapping $\phi: V(G) \rightarrow \{0, 1, 2, \ldots\}$ such that for $1\le i\le l$ and each pair vertices $u, v$ at distance $i$, we have $|\phi(u) - \phi(v)| \geq h_i$. The span $\phi$ the difference between largest smallest labels assigned to by $\phi$, $\lambda_{h_1, h_l}(G)$ defined as minimum over all h_l)$-labellings $G$. In this pap...

Graph labellings form an important graph theory model for the channel assignment problem. An optimum labelling usually depends on one or more parameters that ensure minimum separations between frequencies assigned to nearby transmitters. The study of spans and of the structure of optimum labellings as functions of such parameters has attracted substantial attention from researchers, leading to ...

Many embedded systems have high safety and dependability requirements, which makes ensuring software robustness a top priority in these systems. As embedded computer systems become more complex and incorporate increasing functionality, their software systems become increasingly more difficult to design, build, and maintain. One approach to achieving software robustness is graceful degradation. ...

We establish new lower and upper bounds for the real number graph labelling problem. As an application, we completely determine the optimum spans of L(p, q)-labellings of the infinite triangular plane lattice (solving an open problem of Griggs).

A rooted tree with diameter D is said to have an even degree sequence if every vertex has even degree except for one root and the leaves, which are in the last level D/2 . The degree sequence is said to be quasi even if every vertex has even degree except for one root, every vertex in level D/2 − 1 and the leaves, which are in the last level D/2 . Hrnčiar and Haviar [P. Hrnčiar, A. Haviar, All ...